On Discrete Limits of Sequences of Darboux Bilaterally Quasicontinuous Functions

Abstract

In this article we show that a function $f$, such that the complement of the set of points at which $f$ has the Darboux property and is bilaterally quasicontinuous is nowhere dense, must be the discrete limit of a sequence of bilaterally quasicontinuous Darboux functions. Moreover, there is given a construction of a function that is the discrete limit of a sequence of bilaterally quasicontinuous Darboux functions and which does not have a local Darboux property on a dense set.